Semiparametric interval estimation of Pr[Y > X]

Let X and Y be two independent continuous random variables. We discuss three techniques to obtain confidence intervals for ρ_Pr[Y > X] in a semiparametric framework. One method relies on the asymptotic normality of an estimator for ρ; the remaining methods involve empirical likelihood and combine it with maximum likelihood estimation and with full parametric likelihood, respectively. Finite-sample accuracy of the confidence intervals is assessed through a simulation study. An illustration is given using a dataset on the detection of carriers of Duchenne Muscular Dystrophy